What is the linear velocity if angular veloci | vedclass

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Question

(A) The linear velocity $\vec{v}$ is given by the cross product of angular velocity $\vec{\omega}$ and position vector $\vec{r}$:$\vec{v} = \vec{\omeg

Vedclass · Accepted Answer

$(-18 \hat{i} - 13 \hat{j} + 2 \hat{k})$

Vedclass · Answer

(A) The linear velocity $\vec{v}$ is given by the cross product of angular velocity $\vec{\omega}$ and position vector $\vec{r}$:$\vec{v} = \vec{\omega} 	imes \vec{r}$$\vec{v} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ 3 & -4 & 1 \ 5 & -6 & 6 \end{vmatrix}$Expanding the determinant:$\vec{v} = \hat{i} [(-4)(6) - (1)(-6)] - \hat{j} [(3)(6) - (1)(5)] + \hat{k} [(3)(-6) - (-4)(5)]$$\vec{v} = \hat{i} [-24 + 6] - \hat{j} [18 - 5] + \hat{k} [-18 + 20]$$\vec{v} = -18 \hat{i} - 13 \hat{j} + 2 \hat{k}$

What is the linear velocity if angular velocity $\vec{\omega} = 3 \hat{i} - 4 \hat{j} + \hat{k}$ and position vector $\vec{r} = 5 \hat{i} - 6 \hat{j} + 6 \hat{k}$?

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